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Decomposing Interventional Causality into Synergistic, Redundant, and Unique Components

NeurIPS 2025 · Probabilistic and scientific modeling › Causal discovery · approach: Causal effect identification · 0 citations (OpenAlex)

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Proposes an interventional partial information decomposition of the maximal average causal effect into synergistic, redundant, and unique components via Möbius inversion over the antichain redundancy lattice, illustrated on logic gates, cellular automata, a chemical network, and DistilBERT sentiment completions.

Problem

Observational information decompositions cannot capture true causal power; there is no principled way to split interventional causal effects of multiple variables into unique, redundant, and synergistic parts.

Approach

Define a redundant maximal average causal effect as the minimum MACE over antichain members, then Möbius-invert over the antichain lattice to obtain nonnegative partial causal effects for each antichain, making the decomposition interventional rather than observational.

Key results

• For OR, AND, XOR, and COPY logic gates, the decomposition separates unique, redundant, and synergistic causal power as a function of input probability p; e.g. XOR at p=1/2 is purely synergistic.
• In a chemical network, at low k3 almost all causal power is unique to X1 (k1=10 > k2=1), while at high k3 it becomes mostly synergistic.
• On DistilBERT sentiment completions, 'horribly bad' shows strong negative redundancy, 'not bad' shows positive synergy, and 'really bad' shows unique negative content for 'bad'.

Measured effects reported in the paper

Surprising findings

• Causal power in cellular automata (e.g. Rule 90) depends on the context or initialisation: redundant under one prior and synergistic under another.
• Under the all-zero context, Rule 30 and Rule 54 reduce to OR-like gates, so their causal power becomes fully redundant.

Limitations

• Number of antichains grows with the Dedekind numbers, limiting practical analysis to about five variables.
• Choice of the MMI-based redundancy measure is ambiguous and criticised for simplicity.
• Accurately estimating interventional quantities is hard, so the method requires known causal graphs or simulators.

Experimental setup

Datasets: simulated cellular automata trajectories (100 cells, 10k steps) 25 hand-written base sentences for sentiment completions

Metrics: maximal average causal effect (MACE) partial causal effects per antichain signed causal effect (CE)

Baselines: Williams and Beer I_min minimum mutual information (MMI) Shapley values Chicharro-style observational decomposition

Builds on: Partial Information Decomposition Möbius inversion theorem minimum mutual information (MMI) do-calculus

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